A generalization of leftmost derivation called depth-first derivation is defined. The main result, that the depth-first derivations of an arbitrary phrase-structure grammar generate a context-free language, is proved using a new technique in which families of equivalent depth-first derivations of one grammar are represented by single productions in a new grammar. This result is related to several others, including an analogous result for leftmost derivations, through the theorem of B. Baker [1] that every terminal-bounded grammar generates a context-free language.